One To Many by non primary key. Fail XML Configuration

Question

I have two entities Car and Engine. The Engine contains Set of Cars which use the corresponding Engine.

@Data
@ToString
@EqualsAndHashCode
@NoArgsConstructor
@AllArgsConstructor
public class Engine {
    private int id;
    private String model;
    private int power;
    private Set<Car> cars;
}

@Data
@NoArgsConstructor
@AllArgsConstructor
@ToString
@EqualsAndHashCode
public class Car {
    private int id;
    private String mark;
    private String model;
}

Configurations implemented in hbm.xml format:

<class name="ru.javavision.model.Engine" table="engines">
    <id name = "id" type = "int" column = "id">
        <generator class="identity"/>
    </id>
    <property name="model" column="model"/>
    <property name="power" column="power"/>
    <set name="cars" table="cars">
        <key column="mark" foreign-key="car_mark"/>
        <one-to-many class="ru.javavision.model.Car"/>
    </set>
</class>


<class name="ru.javavision.model.Car" table="cars">
    <id name="id" column="id">
        <generator class="identity"/>
    </id>
    <property name="mark" column="mark"/>
    <property name="model" column="model"/>
</class>

But I got the type error. But I can't figure it out why.

Exception in thread "main" org.hibernate.exception.SQLGrammarException: could not extract ResultSet Caused by: org.postgresql.util.PSQLException: ERROR: operator does not exist: character varying = integer Hint: No operator matches the given name and argument type(s). You might need to add explicit type casts.

In database reference type string on both sides:

CREATE TABLE IF NOT EXISTS cars (
  id    SERIAL PRIMARY KEY,
  mark  VARCHAR(25) UNIQUE NOT NULL,
  model VARCHAR(25)        NOT NULL
);
CREATE TABLE IF NOT EXISTS engines (
  id       SERIAL PRIMARY KEY,
  model    VARCHAR(25) NOT NULL,
  power    INTEGER     NOT NULL,
  car_mark VARCHAR(25) NOT NULL,
  FOREIGN KEY (car_mark) REFERENCES cars (mark)
);

mark and car_mark is VARCHAR but hibernate seen INTEGER. Perhaps he trying mapping by car primary key.

Probably my mistake into Engine XML config somewhere in here:

<set name="cars" table="cars">
    <key column="mark" foreign-key="car_mark"/>
    <one-to-many class="ru.javavision.model.Car"/>
</set>

Perhaps foreign-key attribute doesn't apply and foreign references to id which INTEGER?

Help me find and anderstand my mistake. Thank You!